Analogous to how algebraic speciality indicates the existence of a spinor basis in terms of which various little
group objects \(\Psi ^{(i)}_{abcd}\)  may vanish, within each algebraically special class we can make a finer
classification based on the existence of little group bases \((\alpha _{a}, \beta _{a})\)  for which little group
irreps take special forms. For instance, for certain spacetimes within the type D class it may be possible to
choose a basis \((\alpha _{a}, \beta _{a})\)  such that the only nonzero components of \(\psi ^{(2)}_{abcd}\) 
and \(\chi ^{(2)}_{ab}\)  are \(\psi _{2}^{(2)}\)  and \(\chi ^{(2)}_{1}\) . Precisely such a fine-grained notion of algebraic
speciality, within the coarse type D class, will be of use in proposing a single copy of Kerr-NUT-(A)dS in five
dimensions. That these finer classifications could be important was anticipated already in [1]}.
